Bent functions on a finite nonabelian group

Abstract

We introduce the notion of a bent function on a finite nonabelian group which is a natural generalization of the well-known notion of bentness on a finite abelian group due to Logachev, Salnikov and Yashchenko. Using the theory of linear representations and noncommutative harmonic analysis of finite groups we obtain several properties of such functions similar to the corresponding properties of traditional abelian bent functions.

Keywords and phrases:

• Bent functions
• finite nonabelian groups
• noncommutative harmonic analysis
• Fourier transform